What is the derivative of sqrt(4+3{f)(x}) ?

The derivative of sqrt(4+3{f)(x}) is (3 derivative of {f}(x))/(2sqrt(4+3{f)(x))}

What is the first derivative of sqrt(4+3{f)(x}) ?

The first derivative of sqrt(4+3{f)(x}) is (3 derivative of {f}(x))/(2sqrt(4+3{f)(x))}

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\frac{d}{d x} (4 + 3 f (x))

\frac{3 \frac{d}{d x} ( f ( x ) )}{2 4 + 3 f ( x )}

Solution steps

\frac{d}{d x} (4 + 3 f (x))

Apply the chain rule:

\frac{1}{2 4 + 3 f ( x )} \frac{d}{d x} (4 + 3 f (x))

= \frac{1}{2 4 + 3 f ( x )} \frac{d}{d x} (4 + 3 f (x))

\frac{d}{d x} (4 + 3 f (x)) = 3 \frac{d}{d x} (f (x))

= \frac{1}{2 4 + 3 f ( x )} \cdot 3 \frac{d}{d x} (f (x))

Simplify

\frac{1}{2 4 + 3 f ( x )} \cdot 3 \frac{d}{d x} (f (x)) : \frac{3 \frac{d}{d x} ( f ( x ) )}{2 4 + 3 f ( x )}

= \frac{3 \frac{d}{d x} ( f ( x ) )}{2 4 + 3 f ( x )}

What is the derivative of sqrt(4+3{f)(x}) ?
The derivative of sqrt(4+3{f)(x}) is (3 derivative of {f}(x))/(2sqrt(4+3{f)(x))}
What is the first derivative of sqrt(4+3{f)(x}) ?
The first derivative of sqrt(4+3{f)(x}) is (3 derivative of {f}(x))/(2sqrt(4+3{f)(x))}